Mathematics – Classical Analysis and ODEs
Scientific paper
2012-01-10
Mathematics
Classical Analysis and ODEs
13 pages, no figures
Scientific paper
There exists a remarkable connection between the quantum mechanical Landau-Zener problem and purely classical-mechanical problem of a ball rolling on a Cornu spiral. This correspondence allows us to calculate a complicated multiple integral, a kind of multi-dimensional generalization of Fresnel integrals. A direct method of calculation is also considered but found to be successful only in some low-dimensional cases. As a byproduct of this direct method, an interesting new integral representation for $\zeta(2)$ is obtained.
Kholodenko Arkady L.
Silagadze Z. K.
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